<HTML><HEAD><TITLE>single_pair_shortest_path_bellman_ford(+Graph, +DistanceArg, +SourceNode, +SinkNode, -Path)</TITLE>
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<H1>single_pair_shortest_path_bellman_ford(+Graph, +DistanceArg, +SourceNode, +SinkNode, -Path)</H1>
Computes one shortest path from a source to a sink node (allowing negative distances)
<DL>
<DT><EM>Graph</EM></DT>
<DD>a graph structure
</DD>
<DT><EM>DistanceArg</EM></DT>
<DD>which argument of EdgeData to use as distance: integer
</DD>
<DT><EM>SourceNode</EM></DT>
<DD>source node number
</DD>
<DT><EM>SinkNode</EM></DT>
<DD>sink node number
</DD>
<DT><EM>Path</EM></DT>
<DD>Length-EdgeList structure
</DD>
</DL>
<H2>Description</H2>
<P>
    Computes one shortest path from SourceNode to SinkNode.
    Fails if there is no path at all.  In case of multiple
    shortest paths with the same length, an arbitrary one is returned.
</P><P>
    DistanceArg refers to the graph's EdgeData information that was
    specified when the graph was constructed. If EdgeData is a simple
    number, then DistanceArg should be 0 and EdgeData will be taken
    as the length of the edge. If EdgeData is a compound data structure,
    DistanceArg should be a number between 1 and the arity of that
    structure and determines which argument of the EdgeData structure
    will be interpreted as the edge's length. As opposed to the other
    shortest path algorithms, the Bellman-Ford algorithm can handle
    negative edge lengths, however, the implementation has currently
    no check for negative cycles and will not terminate in that case.
</P><P>
    If DistanceArg is given as -1, then any EdgeData is ignored and
    the length of every edge is assumed to be equal to 1.
</P><P>
    The shortest path is returned as a Length-EdgeList structure
    where Length is the length of the shortest path and EdgeList is that
    path (or one of them) in reverse order, i.e. starting with the edge
    reaching SinkNode and ending with the edge starting from SourceNode.
    </P>
<H3>Modes and Determinism</H3><UL>
<LI>single_pair_shortest_path_bellman_ford(+, +, +, +, -) is semidet
</UL>
<H3>Fail Conditions</H3>
There is no path from SourceNode to SinkNode
<H2>Examples</H2>
<PRE>
    ?- sample_graph(G), single_pair_shortest_path_bellman_ford(G, 0, 1, 3, P).
    P = 2 - [e(2, 3, 1), e(1, 2, 1)]
    </PRE>
<H2>See Also</H2>
<A HREF="../../lib/graph_algorithms/shortest_paths_bellman_ford-4.html">shortest_paths_bellman_ford / 4</A>, <A HREF="../../lib/graph_algorithms/single_pair_shortest_path-5.html">single_pair_shortest_path / 5</A>
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